Filters Menu

0-mean:
remove the continous componant of a signal (its average becomes
NULL)

Band-Pass:
Combination of both HIGH and LOW Pass in cascade, it creates a
band-pass filter

Example
of band-pass [0.02 – 0.1] Hz 4th order

Low-Pass:
Classical, but safe, value in filtering : the Butterworth filter of
2*n order (the order must be even)

Example:
Low-pass filter 4th order, 0.05 Hz

High-Pass:
Butterworth filter of 2*n order, High-Pass

High-pass
0.02 Hz 4th order

Farrer-12-6s:
a combination of low-pass and rejectors, giving very steep slope
near the cut-off frequency, for removing oceanic noise.

Farrer
filter 12-6s 4th order

10%-taper:
the generalized Hanning window : a cosine on half a given period.

Taper
10%

Trend:
For removing trend of a signal with a best fitted polynome of 1
order (it does not introduce dephasage)

Before
Trend order 1 filter

After
Trend order 1 filter: the very long period trend is removed

Polynomial-trend:
removes trend of a signal with a best fitted polynome of n order
(without dephasage)

After
Trend order 3 filter: the very long period trend is better removed
than with order 1

Remove-LTA
(Long Time Average): for removing very long period
oscillations in a signal (like a smooth high pass)

Same
as above, plus remove_LTA filter, this processing remove period with
a cut-off period of 1000s

Modulus
of transfer function of remove_LTA filter

Natural
integrator: the pure mathematical integration, like dividing
the the spectrum by jw, but
it works also in the time domain

Modulus
of transfer function of trapezoidal integrator

Natural
derivator: the pure derivation operator (product by jw),
in the time domain also, with the Z bilinear transform.

Modulus
of transfer function of natural derivator

Integrator
Fc: an integrator with a cutt-off frequency, it avoids the
amplification of the low frequencies to infinite.

Modulus
of transfer function of integrator with 1000s of corner period;
notice the fall of modulus close to Nyquist frequency.

Rejector
Fc: a stable and simple rejector of 2n order, for removing
sharp rai of noise.

Modulus
of transfer function of rejector order 4 at 0.1 Hz

PolePedestal
: this filter is the inverse of the rejector filter of 2n
order, for amplifying sharp rais of signal.

Pole
on pedestal filter is the the inverse effect of a rejector : it
amplifies a sharp frequency band.

Median
filter: a non linear filter for removing stupid individual
points (spikes) in a signal. This filter has a non linear response.

Of course, the
transfer function cannot be calculated by injecting a Dirac as the
input of the filter: It will be removed!

Compensator
1: a filter for compensating instrumental response with order
one.

Compensator
2: a filter for compensating instrumental response with order
two.

Example
of compensator order 2 between 0.1 and 0.02 Hz. Despite of arbitray
unit on the vertical scale (Fourier transform of a Dirac of arbitray
unit convolved with the desired filter), the gain is exactly 1.0
toward the high frequency limit.